Theory of the Proximity Effect in Junctions with Unconventional Superconductors

We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and superconductors. Various possible symmetry classes in a superconductor are considered: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity state. It is shown that the pair amplitude in a DN belongs, respectively, to an ESE, OTE, OTE, and ESE pairing state since only the even-parity $s$-wave pairing is possible due to the impurity scattering.

Figure 1

Local density of states $\rho (\epsilon )$ and pair amplitude $f(\epsilon )$ at the center of the DN, $x=L/2$ is plotted. $\mathrm{Re}f$ and $\mathrm{Im}f$ denote the real and imaginary part of $f(\epsilon )$. The pairing symmetry of the superconductor is (a) ESE, (b) ETO (c) OTE, and (d) OSO, respectively. For (c) and (d), we choose $\overline{C}=0.8$. The resulting symmetry of $f(\epsilon )$ is (a) ESE, (b) OTE (c) OTE and (d) ESE, respectively.